Yes...we have a completely uncovered run (they can get under the coop) and we fold up a tarp and cover part of the run, stapling it against the wind.
It works well, the chickens enjoy it. We've always though about getting some corrugated roofing, though, to hook on top for a more permanent, but removable, solution.

Okay I was thinking that it would probably be a good idea since it's starting to get rather muddy in the run. Mine can also get under the coop where it is dry, but I think they would enjoy more space that was dry. I'll have to work on that today hopefully

The corrugated stuff works great. I hear ya about the rain. I had hoped for an extended summer or warm fall, but I don't think that's going to happen.
Our original coop has a fully covered run---panels of clear and opaque fiberglass, and that is what we will do with the new run, too. It gives shade in the summer, and protects the run area from snow and rain in the winter.